Question

How do you solve `5x - 2y = 10` and `3x + 2y = 6` using substitution?

Answer 1

`x=2 and y=0`

Explanation:

I wonder why you would want to solve this by substitution when elimination is an easier and more obvious method because of the `-2y and +2y` terms.?

Make a single variable the subject:
`3x +2y =6 " "rarr 2y = 6-3x" "rarr color(blue)(y = 3-(3x)/2)`

Substitute this expression for `y` in the first equation:

`5x -2color(blue)(y) =10`

`5x -2(color(blue)(3-(3x)/2)) =10`

`5x -6+3x =10`

`8x = 16`

`x =2`

`color(blue)(y = 3-(3(2))/2`

`y=0`

Compare the Elimination method

`" "5x-2y=10" "....A`
`" "ul(3x+2y =6)" ".....B`
`" "8x " "=16" "larr A+B`
`color(white)(xxxxx.x) x=2`

Substitute in `B`

`3x+2y=6`
`3(2)+2y=6`
`cancel6+2y = cancel6`
`y=0`